Rename parser dir to parse (#3178)

Continuing with #3070. Just a dir and file rename (mostly removing
prefixes, although for parse_tree_fuzzer and parse_tree_file_test I'm
dropping "tree" instead of "parse"). Everything in the parse dir should
be marked as a move.

toolchain/parse/state.cpp

@@ -0,0 +1,14 @@
+// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+// Exceptions. See /LICENSE for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+#include "toolchain/parse/state.h"
+
+namespace Carbon::Parse {
+
+CARBON_DEFINE_ENUM_CLASS_NAMES(State) = {
+#define CARBON_PARSE_STATE(Name) CARBON_ENUM_CLASS_NAME_STRING(Name)
+#include "toolchain/parse/state.def"
+};
+
+}  // namespace Carbon::Parse